### UHG40: Rational trigonometry in three dimensions

We extend rational trigonometry to three dimensions, using a vector approach and the dot product to define quadrance of a vector and spread between two vectors. The main laws of Pythagoras' theorem, the Triple quad formula, the Cross law, Spread law and the Triple Spread formula still apply.However there are some new developments. To motivate this, I recast the spread between two lines in terms of a ratio with a 2x2 determinant, and then introduce the solid spread made by three vectors also in terms of a ratio with a 3x3 determinant.

Length:
31:20